Some properties of spectral measures

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Analysis of orthogonality and of orbits in affine iterated function systems (2006, background): “In contrast, the role of the examples in spectral theory and in Fourier duality is of a later vintage (see e.g., [22, 28 ,30,38]) and there the stability properties are quite different as can be seen from Sect.”
Exponential spectra in L2(μ) (2013, background): “This raises the very interesting question on the existence of an exponential Riesz basis or a Fourier frame for such measures, and more generally for the self-similar measures [15,16,6,25, 10].”
On Fuglede's Conjecture and the Existence of Universal Spectra (2006, background): “Spectral sets can be viewed as special cases of spectral measures, see [ 12 ].”
Spectral property of the Bernoulli convolutions (2008, unknown): “MSC: primary 42C05, 42A65; secondary 28A78, 28A80 Keywords: Bernoulli convolution; Minimal polynomial; Orthogonality; Spectral set; Self-similarity”